How many solutions does this system have?
Exactly one solution
No solution
Infinitely many solutions
Cannot be determined
Correct Answer: C
Choice C is the correct answer. Let's check if one equation is a multiple of the other.
Step 1: Divide the first equation by 3:
This is exactly the second equation!
Step 2: Since both equations represent the same line, every point on that line satisfies both equations.
Conclusion: Infinitely many solutions
💡 Strategic Tip: When equations are scalar multiples of each other (including the constant), they represent the same line.
Choice A is incorrect because one solution requires different slopes.
Choice B is incorrect because no solution requires parallel lines with different constants.
Choice D is incorrect because we can always determine this by simplifying.